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Trixi的菜园：矩形面积与代数分割

Trixi的菜园：矩形面积与代数分割
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2024-06-26 16:55
所属专题 Multiplikation von Binomen
本范例演示如何将一个矩形菜园按不同方式分割成四个子矩形并求面积。学生通过两种方法计算7 m×4 m菜园的面积，使用变量a、b、c、d表示边长并写出面积公式；进一步在8 m×5 m菜园中按长度1∶3、宽度2∶3的比例划分。涉及的核心数学概念包括矩形面积、比例分配以及代数式的展开、合并与提取公因式。构造上使用GeoGebra的Segment、Point、Textfield、LaTeX、If、Rotate等命令，配合输入框与判题对象实现交互。适合七至八年级学生练习代数变形与几何面积的综合性任务。

GeoGebra 命令及参数

  1. IndexOf("$\textsf{Länge\vphantom{Öj}}$", DropDown4) → correct4num
  2. SelectedIndex(DropDown4) → input4
  3. Point(Line[Beet1, v]) → Beet2
  4. Point(Translate[Segment[Beet2, Beet2 + ((2 / 5 * beetx), 0)], vschaufel]) → Schaufel1
  5. Flatten(Sequence[Sequence[Beet1 + (m * (beetx / 5, 0)) + (j * (0, beety / 4)), m, 1, 6], j, 1, 3]) → listpoints
  6. Point(listpoints) → TPoint
  7. Segment((x(Beet5), y(Beet1)) + (streckenabs, 0), (x(Beet5), y(TPoint)) + (streckenabs, 0)) → syRU
  8. Segment((x(Beet5), y(Beet5)) + (streckenabs, 0), (x(Beet5), y(TPoint)) + (streckenabs, 0)) → syRO
  9. Element({1, 2, 3, 4, 5, 6, 7, 7.1, 9, 10, 11, 12, 13, 14, 15}, step2) → step
  10. Textfield(input1) → Eingabefeld1
  11. Textfield(input2) → Eingabefeld2
  12. Point(Line[Garten1, xAxis]) → Garten2
  13. Point(Line[Trixi1, xAxis]) → Trixi2
  14. Textfield(input3) → Eingabefeld3
  15. Textfield(input0) → Eingabefeld0
  16. Point(Line[Beet3, xAxis]) → Beet3b
  17. Point(Translate[Translate[Segment[Beet2, Beet2 + ((2 / 5 * beetx), 0)], vschaufel], vschaufel2]) → Schaufel2
  18. Textfield(input5) → Eingabefeld5
  19. Textfield(input6) → Eingabefeld6
  20. Textfield(input7) → Eingabefeld7
  21. Textfield(input8) → Eingabefeld8
  22. Textfield(input9) → Eingabefeld9
  23. Textfield(input10) → Eingabefeld10
  24. Textfield(input11) → Eingabefeld11
  25. Point(Line[Trixi3, xAxis]) → Trixi4
  26. LaTeX(step, true, true) → Text35
  27. Textfield(input12) → Eingabefeld12
  28. Textfield(input13) → Eingabefeld13
  29. Textfield(input14) → Eingabefeld14
  30. Textfield(input15) → Eingabefeld15
  31. If(step ≟ 2, {Polygon[Beet1, (x(Beet1), y(Beet5)), Beet5, (x(Beet5), y(Beet1))]}, {Polygon[Beet1, (x(Beet5), y(Beet1)), (x(Beet5), y(TPoint)), (x(Beet1), y(TPoint))]}) → beetA
  32. Textfield(input16) → Eingabefeld16
  33. Textfield(input17) → Eingabefeld17
  34. Textfield(input18) → Eingabefeld18
  35. Textfield(input19) → Eingabefeld19
  36. Segment(Beet1 + (0, -0.8), (x(Beet5), y(Beet1) - 0.8)) → sxU
  37. Segment(Beet1 + ((-streckenabs), 0), (x(Beet1), y(TPoint)) + ((-streckenabs), 0)) → syLU
  38. Segment((x(Beet1), y(Beet5)) + ((-streckenabs), 0), (x(Beet1), y(TPoint)) + ((-streckenabs), 0)) → syLO
  39. Segment(Beet1 + (0, (-streckenabs)), (x(TPoint), y(Beet1)) + (0, (-streckenabs))) → sxUL
  40. Segment((x(TPoint), y(Beet1)) + (0, (-streckenabs)), (x(Beet5), y(Beet1) - streckenabs)) → sxUR
  41. Segment(Beet5 + ((6 * streckenabs), 0), (x(Beet5), y(Beet1)) + ((6 * streckenabs), 0)) → syRA
  42. Segment((x(Beet1), y(Beet5)) + (0, streckenabs), (x(TPoint), y(Beet5)) + (0, streckenabs)) → sxOL
  43. Segment((x(TPoint), y(Beet5)) + (0, streckenabs), (x(Beet5), y(Beet5) + streckenabs)) → sxOR
  44. Segment(Beet5 + (streckenabs, 0), (x(Beet5), y(Beet1)) + (streckenabs, 0)) → syRI
  45. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((1 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow1
  46. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((2 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow2
  47. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((3 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow3
  48. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((4 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow4
  49. PointIn(Circle[Pos5, 3]) → Kklein1a
  50. Point(Circle[Kklein1a, 1.7]) → Kklein1b
  51. PointIn(Circle[Pos5, 4]) → Sklein1a
  52. Point(Circle[Sklein1a, 1.5]) → Sklein1b
  53. Corner(PicBeetStep8, 3) → Beet4
  54. Segment((x(Beet3), y(Beet4)) + ((0.2 * streckenabs), streckenabs), (x(Beet4), y(Beet4)) + ((-0.2 * streckenabs), streckenabs)) → bxO
  55. Segment((x(Beet3), y(Beet3)) + ((0.2 * streckenabs), (-streckenabs)), (x(Beet4), y(Beet3)) + ((-0.2 * streckenabs), (-streckenabs))) → bxU
  56. Segment((x(Beet4), y(Beet4)) + (streckenabs, (-0.3 * streckenabs)), (x(Beet4), y(Beet3) + (0.73 * (y(Beet4) - y(Beet3)))) + (streckenabs, (0.3 * streckenabs))) → byO
  57. Segment((x(Beet4), y(Beet3) + (0.73 * (y(Beet4) - y(Beet3)))) + (streckenabs, (0.3 * streckenabs)), (x(Beet4), y(Beet3)) + (streckenabs, (0.3 * streckenabs))) → byU
  58. Segment((x(Beet4), y(Beet4)) + ((5.5 * streckenabs), (-0.3 * streckenabs)), (x(Beet4), y(Beet3)) + ((5.5 * streckenabs), (0.3 * streckenabs))) → byR
  59. PointIn(Circle[Pos13, 3]) → Kklein2a
  60. PointIn(Circle[Pos13, 5]) → Sklein2a
  61. PointIn(Circle[Pos13, 9]) → Bklein1a
  62. Point(Circle[Bklein1a, 1]) → Bklein1b
  63. PointIn(Circle[Pos13, 9]) → Tklein1a
  64. Point(Circle[Tklein1a, 1.3]) → Tklein1b
  65. Point(Circle[Kklein0a, 1.7]) → Kklein0b